How authentic is the aforementioned Hadith, and what is the meaning of: "by your teaching your child the Qur'an," and does it mean teaching people the Qur'an, or disseminating lessons by a shaykh explaining and teaching the Qur'an?

On the Day of Resurrection, the Qur'an will come, weary and pale, to intercede for its reciter who exhausted himself in this world with his fasting and night prayers. It will take its reciter, giving him dominion in his right hand and eternity in his left, and he will be adorned with the crown of dignity and two garments unequaled by the world. This is a reward for him and for his parents for learning and teaching the Qur'an, whether the parents taught their child, or the child taught others, or the child himself learned. For one who points to good is like its doer, and the best of that is teaching people sacred knowledge.